Đáp án:
\(-1792\).
Giải thích các bước giải:
\(\begin{array}{l}
C_{n - 4}^{n - 6} + n.A_n^2 = 454\,\,\left( {n \ge 2} \right)\\
\Leftrightarrow \frac{{\left( {n - 4} \right)!}}{{2!\left( {n - 6} \right)!}} + n.\frac{{n!}}{{\left( {n - 2} \right)!}} = 454\\
\Leftrightarrow \frac{{\left( {n - 4} \right)\left( {n - 5} \right)}}{2} + n.n\left( {n - 1} \right) = 454\\
\Leftrightarrow {n^2} - 9n + 20 + 2{n^3} - 2{n^2} = 908\\
\Leftrightarrow 2{n^3} - {n^2} - 9n - 888 = 0\\
\Leftrightarrow n = 8\,\,\left( {tm} \right)\\
{\left( {\frac{2}{x} - {x^3}} \right)^8} = \sum\limits_{k = 0}^8 {C_8^k{2^k}{x^{ - k}}{{\left( { - 1} \right)}^{8 - k}}{x^{24 - 3k}}} \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sum\limits_{k = 0}^8 {C_8^k{2^k}{{\left( { - 1} \right)}^{8 - k}}{x^{24 - 4k}}} \\
He\,\,so\,\,cua\,\,{x^4}\,\,ung\,\,voi\,\,24 - 4k = 4 \Leftrightarrow k = 5\\
Vay\,\,he\,\,so\,\,cua\,\,{x^4}\,\,la:\,\,C_8^5{.2^5}.{\left( { - 1} \right)^3} = - 1792.
\end{array}\)
